Questions tagged [options]
A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.
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What is delta of an option signaling?
In an interview I was once asked what the delta of an option was and my answer started from the fact that it is the first derivative of the option with respect to the price, and then I concluded ...
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Alternatives to RDBMS for options backtesting
I've assembled a large dataset (~2B+ records) of options price data in MySQL for backtesting purposes.
At a number of points, due to the sheer amount of data being retrieved and filtered, processing ...
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How is Emanuel Derman's implied tree model implied volatility skew derived?
I am reading Emanuel Derman's paper Patterns of Volatility Change. The section, Implied Volatility In The Sticky Implied Tree Model has the linear skew approximation near the old underlying $S_0$
$$\...
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Using delta as probability of an option expiring in the money
I understand that delta can be seen as a probability proxy for an option expiring in the money, as well as deltas for call options ranging from 0 to 1 and deltas for put options ranging from 0 to -1.
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what is option zeta?
Is this an option greek? I've come across this term in some option book, and also online definition e.g. HERE:
A measure that captures the premium difference between the value of an
option calculated ...
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Reference for path dependent options
I want to study path dependent options for which I am following the book Paul Wilmott on Quantitative finance.But here I dont find the detailed explanations or derivations for the various PDEs .So is ...
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Difference in pricing of American call and put
In Paul Wilmotts quantitative finance books he says that the the value of an American option satisfies the following
$$
\frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2 \frac{\partial^2V}{\partial ...
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How to price a risk reversal for common dice gain with chance to re-roll
I was just thinking about an extension to the common dice throwing interview expected value question:
Question: Imagine a game where you throw a die and get a payoff equal to the number shown by the ...
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Independent variable in pricing of strongly path dependent options
I am reading Paul Wilmott on quantatative finance where he discuss the pricing of strongly path dependent options.The payoff at expiry T depends on the path taken by the asset in the sense that it ...
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How to derive the relationship between gamma and theta?
I am trying to derive this formula Θ = –0.5 × Γ × S^2 × σ^2 to see where it comes from.
My thinking is that PnL = delta dS + Vdσ + 0.5Γ(dS)^2 + Θdt.
Assume we delta hedged and vega hedged, first and ...
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MOC or TAS mechanism to trade stock options?
Wonder if anyone can help. Is there a product or mechanism to trade cleared stock options at the settlement price, in the same manner to Market on Close orders or Trade at Settle on commodity markets?...
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Computing the denominator of diluted earnings per share
I'm practicing for CFA level 1, and I faced this question. I don't understand the last part (802 − 481 = 321) because I understand that a company doesn't realize options of its own shares, if you are ...
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What does it mean to be long the skew?
Consider an equity option such as SPY and I'm long the skew, do I make money if puts raise in price and calls decrease or the opposite?
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How is delta defined as a unit?
This is going to be a embarrassingly basic question. But the answer seems to be hard to find.
What does, say, selling, $d$ delta of calls mean? How is the "delta" defined? I am not asking ...
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Best way to measure time to expiration for options?
From my reading it seems that only trading days should be accounted for when calculating time to expiration. On the other hand, I see that VIX is calculated using every day until expiration without ...
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Early exercise American Options with Dividend
this is a basic question but I have not fully understood it.
Let's say we have dividend paying stock (continuous dividend yield), when would we exercise the Option early? Since the Dividend yield is ...
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Question about pricing forward start option with Heston Monte Carlo
I'm trying to price a forward start option with payoff $\Big(\dfrac{S_{T_2}}{S_{T_1}}-1\Big)^+$ with Heston Monte Carlo.
Heston Model:
$$ dS_t = rS_tdt + \sqrt{v_t}S_tdW_t^1$$
$$ dv_t = \kappa(m-v_t) +...
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Montecarlo pricing
I have some problems with the Montecarlo simulation to price a generic Call option. I want to explain something regarding MC simulation with a simple cases, and after that I am going to talk about my ...
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Delta hedging the day before expiry
In practice, how do people usually delta hedge options the day before expiry? Would you still use the black Scholes delta and then close out the position in the underlying immediately after expiry? ...
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Equivalence of expectation condition for contingent claims attainable and contingent claims super replicable
We have the following definitions for set of contingent claims attainable and contingent claims super replicable
I want to prove the following result
How do I show iii $\implies $ ii.I understand ...
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Better to "work order" or just give best limit price when placing multi-leg option orders through IB with SMART routing
I place option trades usually consisting of 2-4 legs...mostly ratios spreads through IB using the SMART routing algorithm. Say for a particular trade, the bid is 0.04 debit and the ask is 0.17 debit. ...
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No free lunch with bounded and vanishing risk
I am reading a book which states 'No free lunch with bounded risk as follows
where $\tilde{V}_t$ is the discounted value of the portfolio.Then it states the following theorem
EMM is the equivalent ...
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What is the number of nodes, which have to evaluated, in a binomial tree for an option on dividend-paying stock?
In John Hull's book "Options, futures and other derivatives" 10th Edition, Chapter 21, there are two examples, on how binomial trees on dividend-yield stock option look like.
The first ...
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Vol, Gamma, Vega -- essentially all the same?
When talking to traders I hear this sentence a lot
I am a buyer/seller of X
where X = {vol, gamma, vega}
Is X basically all the same -- they are just saying -- I think implied volatility is cheap or ...
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Path-dependent options valuation
Assume that we have an arbitrage-free and complete market. The well known formula for the arbitrage-free price of an attainable derivative $X$ at time $0 \leq t \leq T$ is given by:
\begin{align*}
V(t)...
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Proving the discounted stock price is martingale
Let $\mathcal{K}_s$ be
$$ \mathcal{K}_s=\{\tilde{V}_t(\theta):0\leq t<\infty,\,\theta\text{ a simple strategy}\},$$
where $\tilde{V}_t(\theta)$ is the discounted value process of the self financing ...
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Rationale for the CMS Spread and CMS Rate as being underlying for Dual Range Accrual?
I was searching on the products issued by the banks to retail investors, and saw some of the Dual Range Accruals having underlying as USD CMS 30Y - 2Y, and USD CMS 10Y, each having low barrier and ...
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Why is gamma exposed through the square of spot prices?
As per this article, "the mathematically intuitive way to expose gamma is through the square of the underlying price": https://llllvvuu.dev/blog/unbundling-gamma
Can someone explain this? ...
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Net delta and gamma profile of a put spread
I have a question regarding the description in Simon Gleadall's book -- option gamma trading which you can find a copy HERE.
The following paragraph he discussed about gamma and delta profile of a ...
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Why a long-dated option has delta > 0.5?
Each option book states that the delta, considered as the hedge ratio and not the probability to have the option exercised, is 50% for ATM options. Anyway, empirically speaking I see it is more than ...
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FX options: is convexity usually heavily overpriced?
I have access to daily vol quotes for EURUSD options from 2006 to today. I was playing around with them and constructed a "daily rolled backtest" for various options constructs, like ...
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Is publication of Black-Scholes in 1973 and founding of CBEO in 1973 coincidental?
Apparently, CBOE was founded in 1973 and opened on 1st January that year (source = Google), to start trading listed options.
The famous Black-Scholes paper was published also in 1973.
I am wondering ...
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Historical Options data
Are there any good sources where I can obtain daily historical options data (strike price, expiration dates, bid/ask spread, etc).
I understand that this type of data is very hard to come by and ...
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Early expiry option implied volatility
I’m new to this forum so first of all I wanna welcome everyone here.
I am a commodity trader, mostly covering option books (vanilla and structured one) and I would ask more expert people how they can ...
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Temporal and Intrinsic value with Options on Futures
I'm working with this options: ICE PDB Options, those are options on futures (Options that automatically exercise intro the settlement price of the Future on the day of expiry)
In this way the ...
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Question in convex arbitrage [closed]
In convex arbitrage, we say that if the convexity of call(put) price as a function of the strike is violated, we can have arbitrage strategy. For instance,
$$
C_{K_2}\geq \lambda C_{K_1}+(1-\lambda) ...
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What happens when you buy call options on a stock that does a stock split
suppose i say lyft in 2023 will be worth more then 50 per share (the current call price for the option). suppose im right and each share is worth 75, but in the interim lyft announces a 2-1 stock ...
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Model independent (or reasonable assumption) bounds on OTM put price given an ATM call price
I am looking for model independent (or weak/reasonable assumption) bounds on price of a OTM vanilla put on strike $k1$, conditional on an observable price for a ATM call at some strike $k2$. I ...
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How can we argue that the "economic" risk-neutral argument doesn't introduce arbitrage?
I am wondering why when use the "economic" risk neutral argument, we don't introduce arbitrage. By "economic" I mean an argument that doesn't use stochastic calculus or equivalent ...
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Relationship between VIX and Vega
Assuming that all other factors (such as underlying price, strike price, etc.) remain unchanged, I want to see how a spike in VIX would affect the price of the average call option? Assume Vega is ...
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How to measure accuracy of SABR volatility surfaces?
I would like to test how accurate are SABR volatility surfaces with respect to historical volatility over a given time period and for a specific equity index.
Reading a few papers I realised that one ...
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What happens to options on a SPACs unit class post deal closure?
SPAC unit share classes are typically structured as following:
Unit = Stock + (1/5) Warrant
When the SPAC deal closes the ticker changes and the unit converts to ...
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How to derive Parameter Derivative within an FFT integral
I have the following function (Carr-Madan) of which I am trying to take the derivative wrt $\theta$:
$c(k)=\int_0^\infty \frac{e^{-iuk}}{\alpha^2 + \alpha - u^2 + i(2\alpha+1)u} e^{\phi_T(u-(\alpha+1)...
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Compare rich / cheap options on 2 underlyings
this question can turn out to be very basic but its something that has been bugging me.
Say I want to buy/sell an option on A vs sell/buy an option on B.
Facts I know
A and B are different ...
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Industry standards for vol control index options
Consider an index of the type:
$I(t)/I(t-1) = 1+ a(t) (S(t)/S(t-1)-1)+(1-a(t))r(t-(t-1))$
It is arbitrarily initialized. $r$ is the risk free rate.
a(t) is determined piecewise as:
$a(t)=s_{target}/s_{...
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Is there an equation that gives you the optimal spread width or strike prices when opening a vertical options spread?
On a specific leg, when going to open a spread is there an equation that can tell me at what strike price I should sell at and what strike price I should buy at?
I look at this options calculator ...
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Finite Difference Method in Greeks (Options)
I need a way to approximate the analytical formula of Greeks of a generic call option using the Finite Difference Method.
For example, the FD method for Delta/Gamma is the following one:
Now, I am in ...
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IV on FOP (futures options) being higher than IV on equivalent ETF
I've been observing that options on /es has a higher IV than the options on SPY even though they're both tracking the S&P 500. What causes this? Doesn't this mean that the options on /es is more ...
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Exotics - Combination of different payoffs using Black-Scholes
I'm currently struggling with the derivation of a formula to price the following exotic option with Black-Scholes.
The option has the maximum payoff of $(S_T-z)$ and $(y - S_T)$, where $S_T$ is the ...
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Perpetual Option Price under Black Scholes model
Would like to ask you, how would you price an Option which has its starting underlying price S0 = 70 dollars, with no dividends, and that pays 0.5 dollars each time the underlying price hits a barrier ...
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